The most significant consideration in the use of prosthetic or therapeutic devices in cardiovascular organs is the exposure of blood to an artificial surface. Immediately upon contact, blood platelets aggregate onto the surface by binding with adsorbed adhesive proteins. This process becomes clinically significant when an embolus breaks off, traveling downstream until becoming lodged in a small artery and causing organ damage due to loss in blood supply. Typically, biomaterials are in contact with flowing blood, and the nature of this flow affects the deposition process. By understanding exactly how the dynamics of the flow influences platelet deposition, cardiovascular devices can be designed to minimize the adverse effects of their use in contact with blood. The objective of this study is the development of a mathematical model of platelet kinetics and deposition onto surfaces exposed to complex flow conditions, so that a more complete, quantitative description of the thrombotic process may be obtained and used to optimize cardiovascular device design for minimal thrombotic potential. The model will include terms that represent three general mechanisms evidence in experimental measurements: 1) transport of platelets and other clotting agents to the surface, 2) reaction with the surface through activation and binding with adhesive proteins, and 3) possible detachment from the surface by fluid momentum, dissolved species mass, and particulate mass, to the surface. Modeling of platelet activation and binding to adhesive proteins adsorbed on the surface provides for mechanism #2. Finally, mechanism #3 is modeled by requiring above- threshold values of wall shear stress and local thrombus height for detachment of adherent platelets. Flow solutions will be verified by comparison with experimental measurements. The model will be validated and model parameters determined using data available in the literature for classical flow conditions that isolate each mechanism: abrupt expansion (mass transport), Poiseuille flow (surface reactivity), and the Couette flow (fluid shear). Finally, the model will be implemented using an arterial stenosis geometry, and the efficacy of the model to adequately represent the hallmarks evident in experimental measurements will be assessed through parametric analysis and comparison with measurements already obtained in the PI's laboratory.